Exit age distribution

This is defined as the fraction of material in the outlet stream that has been in the system for the period between t and t + dt, and is equal to E(t)dt, where E(t) is called the exit age distribution function of the fluid elements leaving the system. This is expressed as... 

The eumulative exit age distribution is a non-negative, monotone non-deereasing funetion as shown in Figure 8-3. 

The exit age distribution funetion E(t) is obtained from outside the vessel while the internal age distribution funetion I(t) is obtained from inside the vessel. I(t) ean be represented in terms of the RTD or the F-eurve as... 

The exit age distribution funetion E(t) for a laminar flow reaetor is... 

Eor the exit-age distribution, the fraction of material exiting the system from the three CSTRs that are in the system between t and t -I- 6t is ME(t)6t = uC3(t)6t or... 

For all likely operating conditions, (ie., for t < X), the appropriate values of the concentration and the polymerization rate constant are the values calculated at t = t ( 2). To prove this, the exit age distribution function for a backmix reactor was used to weight the functions for Cg and kj and the product was integrated over all exit ages (6). It is enlightening at this point to compare equation 18 with one that describes the yield attainable in a typical laboratory semibatch reactor at comparable conditions. ... 

A curve showing the differential weight fraction versus chain length for the batch-prepared polystyrene is given in Figure 3. Figure 4 illustrates the exit age distributions obtained from the RTD experiments with benzene and with a 30 weight percent polymer solution. 

Via a passive scalar method [6] where or, denotes the volume fraction of the i-th phase, while T, represents the diffusivity coefiBcient of the tracer in the i-th phase. The transient form of the scalar transport equation was utilized to track the pulse of tracer through the computational domain. The exit age distribution was evaluated from the normalized concentration curve obtained via measurements at the reactor outlet at 1 second intervals. This was subsequently used to determine the mean residence time, tm and Peclet number, Pe [7]. 

To establish the validity of the numerical scalar technique for RTD analysis, the normalized exit age distribution curve of both counter-current (Figure 1 (a-b)) and cocurrent (Figure 1 (c-d)) flow modes were compared. Table 1 shows that a good agreement was obtained between CFD simulation and experimental data. 

The exit-age distribution function is a measure of the distribution of the ages of fluid elements leaving a vessel, and hence is an RTD function. As a function of time, f, it is defined as ... 

Figure 13.2 Exit-age distribution function E(t) for arbitrary (nonideal) flow showing significance of area under the E(t) curve...

The exit-age distribution function may also be expressed in terms of dimensionless time 8 defined by... 

Fig. l.(a) Histogram of residence times, and (b) limiting form of this histogram giving the exit age distribution, E(f). 

It is evident that elements of fluid taking different routes through the reactor may take different lengths of time to pass through the vessel. The distribution of these times for the stream of fluid leaving the vessel is called the exit age distribution E, or the residence time distribution RTD of fluid. E has the units of time" ... 

Figure 11.6 The exit age distribution curve E for fluid flowing through a vessel also called the residence time distribution, or RTD.

The concentration readings in Table Ell.l represent a continuous response to a pulse input into a closed vessel which is to be used as a chemical reactor. Calculate the mean residence time of fluid in the vessel t, and tabulate and plot the exit age distribution E. 

Problem 1, If the input signal is measured and the exit age distribution functions E, E, and E are known, then Q is the convolution of E with and so on, thus... 

Each flow pattern of fluid through a vessel has associated with it a definite clearly defined residence time distribution (RTD), or exit age distribution function E. The converse is not true, however. Each RTD does not define a specific flow pattern hence, a number of flow patterns—some with earlier mixing, others with later mixing of fluids—may be able to give the same RTD. 

Scheme Q D, and E, From Fig. 12.1 the exit age distribution function for the two equal-size plug-mixed flow reactor system is...

For a series of equal-sized backmix reactors the exit age distribution function is... 

For flow with arbitrary exit age distribution E(t) Eq. (144) must be solved directly. A convenient graphical method for doing this has been devised by Schoenemann (S9) who then discusses the application of this method to some industrial reactors. The direct use of Eq. (144) is also illustrated by Levenspiel (L13), Sherwood (S13) and Petersen s (P5) treatment of catalyst-activity levels in regenerator-reactor systems. 

Db R) Radial dispersion coefficient, general dispersion model in cylindrical coordinates Molecular diffusivity Exit age distribution function, defined in Section I... 

The distribution of residence times for a stream of fluid leaving a vessel is called the exit age distribution function E (synonymous with residence time distribution or... 

Fig. 2.3. Exit age distribution function or E-curve also known as the residence time distribution...

The fluidised bed will be considered as a continuous stirred tank reactor in which ideal macromixing of the particles occurs. As shown in the section on mixing (Chapter 2, Section 2.1.3), in the steady state the required exit age distribution is the same as the C-curve obtained using a single shot of tracer. In fact the desired C-curve is identical with that derived in Chapter 2, Fig. 2.3, for a tank containing a liquid with ideal micromixing, but now the argument is applied to particles as follows ... 

Fig. 3.38. Flow of particles through a fluidised bed showing a normalised C-curve which is identical with the exit age distribution function E...

By definition the exit age distribution function E is such that the fraction of the exit stream with residence times between t and t + St is given by Ed/. 

Volume of voids per total surface area Exit age distribution... 

Figure 3.78 Exit age distribution function at different measuring points of the screening set-up [111] (by courtesy of AlChE).

Figure 3.79 Dimensionless exit age distribution function using tubular reactors with different inner diameters [111] (by courtesy ofAIChE).

The exit-age distribution function E(t) is approximately obtained by following the experimentally often used method of backward differencing ... 

E E(t) EDM EDTA EDX EHD EKI EO EOF ESI-MS Ez Activation energy Exit-age distribution function Electro-discharge machining Ethylene-diamine-tetraacetic acid Energy dispersive X-ray Electrohydrodynamic Electrokinetic instability Electroosmotic-Electroosmotic flow Electrospray ionization mass spectrometry Electric field... 

---